Problem: Solve for $x$ : $3x^2 - 45x + 150 = 0$
Answer: Dividing both sides by $3$ gives: $ x^2 {-15}x + {50} = 0 $ The coefficient on the $x$ term is $-15$ and the constant term is $50$ , so we need to find two numbers that add up to $-15$ and multiply to $50$ The two numbers $-5$ and $-10$ satisfy both conditions: $ {-5} + {-10} = {-15} $ $ {-5} \times {-10} = {50} $ $(x {-5}) (x {-10}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x -5) (x -10) = 0$ $x - 5 = 0$ or $x - 10 = 0$ Thus, $x = 5$ and $x = 10$ are the solutions.